Related papers: The tail process and tail measure of continuous ti…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…
We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling features commonly found in observed financial returns. The extremal properties of these processes are of considerable interest for…
The tail process $\boldsymbol{Y}=(Y_{\boldsymbol{i}})_{\boldsymbol{i}\in\mathbb{Z}^d}$ of a stationary regularly varying random field $\boldsymbol{X}=(X_{\boldsymbol{i}})_{\boldsymbol{i}\in\mathbb{Z}^d}$ represents the asymptotic local…
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete…
Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH…
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…